Question

There are two vectors. The first one has initial and terminal points as A(–1, 3), B(2, 4) respectively. The second one has initial and terminal points as. C(1, -2), D(4, -1) respectively. The two vectors are not equal vectors.

• A. True
• B. False

Answer 1

The correct option is B False

First vector $\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$ (Using triangle law for vector addition)
= ((2 - (-1)), (4 - 3))
= (3, 1)
$\left|\overrightarrow{AB}\right|=\sqrt{(3{)}^2+(1{)}^2}$
$=\sqrt{10}$.
Second vector $\overrightarrow{CD}=\overrightarrow{OD}-\overrightarrow{OC}$ (Using triangle law for vector addition)
= ((4-1), (-1-(-2)))
= (3, 1)
$\left|\overrightarrow{CD}\right|=\sqrt{3^2+1^2}$
$=\sqrt{10}$
So $\left|\overrightarrow{AB}\right|=\left|\overrightarrow{CD}\right|$
Now only equal magnitude doesn't make them equal vectors. They have to have the same directions as well for equality to hold.
If $\overrightarrow{AB}$ and $\overrightarrow{CD}$have same slope, that means they have same directions.
Slope of $\overrightarrow{AB}=\frac{4-3}{2-(-1)}=\frac{1}{3}$
Slope of $\overrightarrow{CD}=\frac{-1-(-2)}{4-1}=\frac{1}{3}$
So their magnitude and direction are same.
So $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are equal vectors.